Unit 4 reviews and builds on children's understanding of tens and extra ones. Children explore tens-and-ones groupings. Activities provide repeated experience in building multi-digit numbers in a variety of contexts with strong visual support. Children then begin to make the connection between these groupings and their numerical representation. This connection will help them master the concept of place value.

In English, teen and 2-digit number words are complex and difficult to learn. In contrast, in some Asian languages the word for 13, for example, translates into "ten three". In the English system, teen and 2-digit numbers look like two single-digit numbers written beside each other; nothing shows the ten value for the digit on the left. Young children need verbal and visual supports for understanding these number words and written numbers, a process we begin in Kindergarten. In Math Expressions, we provide this scaffolding by using tens and ones words, as well as standard number words, when working with teen and 2-digit numbers. We say 13 as thirteen and as 1 ten 3 ones and say 38 as thirty-eight and 3 tens 8 ones. These words are used interchangeably and help reinforce the embedded ten-based thinking and place value understanding.

Place Value
It is absolutely essential that children develop a solid understanding of the base-ten numeration system and place-value concepts by the end of grade 2. Children need many instructional experiences to develop their understanding of the system, including how numbers are written. They should recognize that the word ten may represent a single entity (1 ten) and, at the same time, 10 separate units (10 ones) and that these representations are interchangeable.

Groups of Ten
One of the first steps in mastering numbers to 100 involves learning the names of the decade numbers (10, 20, 30,...) and making the association between these words and the corresponding tens they represent (1 ten, 2 tens, 3 tens, ....) With this knowledge, children are soon able to add tens mentally (30 + 40 = 3 tens + 4 tens). These skills are introduced and practiced with visual supports such as a 10 x 10 grid, or finger flashes.

Tens and Ones
After learning the decade numbers, children begin building an integrated concept of tens and ones starting with the teen numbers. Integrating tens and ones into 2-digit numbers represents an enormous conceptual advance over simply counting by tens, and this skill takes practice. In Unit 4, practice is provided in a variety of ways as children repeatedly link tens groupings to concrete quantities, number words, and written numbers. In this way, they begin to construct the complex web of meanings and symbols that make up 2-digit numbers. Children begin to draw tens (sticks) and ones (circles) to represent number quantities. This allows them to visualize the meaning of the numbers and understand the separate functions of the tens and ones in our number system. The system evolves gradually from the Dot Array on the MathBoard to free hand representations.

Problem-Solving Strategies
The problems in this unit are carefully sequenced to allow children to understand the number concepts and to avoid reliance on rote mechanical procedures. Math drawings and Math Talk support understanding.

In English, teen and 2-digit number words are complex and difficult to learn. In contrast, in some Asian languages the word for 13, for example, translates into "ten three". In the English system, teen and 2-digit numbers look like two single-digit numbers written beside each other; nothing shows the ten value for the digit on the left. Young children need verbal and visual supports for understanding these number words and written numbers, a process we begin in Kindergarten. In

Math Expressions, we provide this scaffolding by usingtensandoneswords, as well as standard number words, when working with teen and 2-digit numbers. We say 13 asthirteenand as1 ten 3 onesand say 38 asthirty-eightand3 tens 8 ones.These words are used interchangeably and help reinforce the embedded ten-based thinking and place value understanding.Place ValueIt is absolutely essential that children develop a solid understanding of the base-ten numeration system and place-value concepts by the end of grade 2. Children need many instructional experiences to develop their understanding of the system, including how numbers are written. They should recognize that the word

tenmay represent a single entity (1 ten) and, at the same time, 10 separate units (10 ones) and that these representations are interchangeable.Groups of TenOne of the first steps in mastering numbers to 100 involves learning the names of the decade numbers (10, 20, 30,...) and making the association between these words and the corresponding tens they represent (1 ten, 2 tens, 3 tens, ....) With this knowledge, children are soon able to add tens mentally (30 + 40 = 3 tens + 4 tens). These skills are introduced and practiced with visual supports such as a 10 x 10 grid, or finger flashes.

Tens and OnesAfter learning the decade numbers, children begin building an integrated concept of tens and ones starting with the teen numbers. Integrating tens and ones into 2-digit numbers represents an enormous conceptual advance over simply counting by tens, and this skill takes practice. In Unit 4, practice is provided in a variety of ways as children repeatedly link tens groupings to concrete quantities, number words, and written numbers. In this way, they begin to construct the complex web of meanings and symbols that make up 2-digit numbers. Children begin to draw tens (sticks) and ones (circles) to represent number quantities. This allows them to visualize the meaning of the numbers and understand the separate functions of the tens and ones in our number system. The system evolves gradually from the Dot Array on the MathBoard to free hand representations.

Problem-Solving StrategiesThe problems in this unit are carefully sequenced to allow children to understand the number concepts and to avoid reliance on rote mechanical procedures. Math drawings and Math Talk support understanding.

Fuson, Karen,

Math Expressions, Unit 4 Overview